Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: What the test question that just bugged the crap outta me

  1. Sep 28, 2005 #1
    we were given the DE y'=2sqrt(y) that was how it was given, I didn't take the square root myself and thus forget a +and-

    so using a bernoulli equation I got (x+c)^2(I think, I'm doing this from memory)

    then the next part asked to find two solution curves for the point (1,1), so x^2 and (x-2)^2, right?

    THEN it asked for the solution guaranteed by the existance and uniqueness theorem at (1,1), but didn't I just find TWO solution curves for that same point, which means there ISN'T an unique solution? And to further confuzzle matters if I actually apply the theorem it seems like it SHOULD have an unique solution at (1,1)
     
  2. jcsd
  3. Sep 28, 2005 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Take a closer look at the solution [itex]y=(x-2)^2[/itex]. It has a negative slope at [itex]x=1[/itex]. If [itex]y'<0[/itex], then according to your DE [itex]2\sqrt{y}<0[/itex], which is impossible.
     
  4. Sep 29, 2005 #3
    aw hell, so when it asked me to sketch two solution curves THAT was the "trick" question?
     
  5. Sep 30, 2005 #4
    or were they both solution curves but they passed through the point or something? We'll go over it on Monday but I hate waiting to know
     
  6. Sep 30, 2005 #5

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    They are not both solutions at [itex]x=1[/itex]. [itex]y=(x-2)^2[/itex] simply does not satisfy the differential equation at [itex]x=1[/itex]. What happened was that you introduced an extraneous root when you squared [itex]y^{1/2}[/itex].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook